Several novel compact multiple-band High-impedance surface EBG structures are presented. By utilizing S-shape corrugated arms embedded on the square patch or spiral arms to increase the inductance, the resonant frequency of EBG structure will be reduced. In order to broad the width of stopband and adjust the ratio of the centre frequencies for multi-band EBG, a log periodic distance for S-shape strip arms is designed. Some parameters of EBG structure for the effects of bandstop width are discussed in detail. The results show that the proposed novel EBG structure can provide more multiple bandgap and reduce the EBG size for a fixed periodicity. This proposed EBG can be much significantly applied on the multiple frequency antennas and low frequency antennas.